Pore structure model for elastic wave velocities in fluid‐saturated sandstones

Abstract

During hydrostatic compression conducted within the elastic regime, P and S‐wave velocities measured on porous rock samples generally increase with pressure and reach asymptotic values at high pressures. The increase in velocities can be attributed to the gradual closure of compliant cracks, in which case the high‐pressure velocities reflect only the influence of the stiff, non‐closable pores. A procedure is presented to extract the complete pore aspect ratio distribution from the pressure dependence of dry velocities, assuming that the rock contains a distribution of cracks with different aspect ratios, and one family of stiff pores having an aspect ratio that generally will lie between 0.01 and 1. The model is able to invert successfully many sets of experimental data on dry sandstones taken from the literature. The pore aspect ratio distribution inverted from dry data can then be used to predict saturated velocities as functions of pressure, by introducing fluid into the pores. For ultrasonic velocity measurements that are performed at high frequencies in the laboratory (∼ MHz), the predictions of saturated velocities using effective medium theories match well the experimental data for a good number of sandstone data sets. The saturated velocities thus predicted are always more accurate than those predicted from the Gassmann relations, which underpredict the saturated velocities by a large amount. These results are only weakly dependent on the choice of the effective medium theory.